Unraveling Quantum Brownian Motion: Pointer States and their Classical Trajectories

We characterize the pointer states generated by the master equation of quantum Brownian motion and derive stochastic equations for the dynamics of their trajectories in phase space. Our method is based on a Poissonian unraveling of the master equation whose deterministic part exhibits soliton-like solutions that can be identified with the pointer states. In the semiclassical limit, their phase space trajectories turn into those of classical diffusion, yielding a clear picture of the induced quantum- classical transition.